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11 Aug 2025, 08:39
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
50% (01:30) correct
50% (01:25) wrong based on 2 sessions
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“A number squared is equal to at least twice the number.” Which of the following numbers satisfy this statement?
Indicate all such numbers.
A. \(10^{-2}\)
B. 0.9
C. 1
D. 2
E. 3
F. \(10^8\)
Indicate all such numbers.
A. \(10^{-2}\)
B. 0.9
C. 1
D. 2
E. 3
F. \(10^8\)
24 Aug 2025, 05:26
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Official Explanation
The question asks, when is \(n^2 ≥ 2n.\) Since we are only considering positive values of \(n,\) we can divide both sides by \(n\) to obtain \(n ≥ 2.\) Thus, the statement is satisfied for values of \(n\) greater than or equal to 2, (D), (E), and (F).
*\(10^{-2}\) means (A) and (B) are not correct because squaring 0.01 or 0.9 yields an even smaller value, certainly not \(“at least twice the number.” \) (C) is not correct because 12 = 1, whereas twice 1 equals 2. (D) is correct, because \(2^2 = 4,\) which is exactly twice 2, or 2 × 2, and a number is at least equal to itself. (E) and (F) are correct, because if \(n > 2,\) then \(n^2 = n × n > n × 2.\)
Answer: D,E,F
The question asks, when is \(n^2 ≥ 2n.\) Since we are only considering positive values of \(n,\) we can divide both sides by \(n\) to obtain \(n ≥ 2.\) Thus, the statement is satisfied for values of \(n\) greater than or equal to 2, (D), (E), and (F).
*\(10^{-2}\) means (A) and (B) are not correct because squaring 0.01 or 0.9 yields an even smaller value, certainly not \(“at least twice the number.” \) (C) is not correct because 12 = 1, whereas twice 1 equals 2. (D) is correct, because \(2^2 = 4,\) which is exactly twice 2, or 2 × 2, and a number is at least equal to itself. (E) and (F) are correct, because if \(n > 2,\) then \(n^2 = n × n > n × 2.\)
Answer: D,E,F
